Reading and writing large numbers (up to 7–8 digits).

Reading & Writing Large Numbers (up to 8 Digits)

Subtopic Navigator

Lesson Objectives

  • Understand the place value of ten-millions, millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones in 7-8 digit numbers.
  • Read and write 7-8 digit numbers in words and digits.
  • Express 7-8 digit numbers in expanded form (e.g., 34,567,890 = 30,000,000 + 4,000,000 + 500,000 + 60,000 + 7,000 + 800 + 90 + 0).
  • Compare and order 7-8 digit numbers up to 100,000,000 using symbols (>, <, =).
  • Round large numbers to the nearest ten, hundred, thousand, ten-thousand, hundred-thousand, million, and ten-million.

Introduction to Large Numbers

A 7-digit number has seven digits: millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones. An 8-digit number has eight digits: ten-millions, millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones. The largest 7-digit number is 9,999,999, and the largest 8-digit number is 99,999,999. Understanding these numbers helps us work with population counts, national budgets, distances between cities, and scientific measurements.

Key Concepts for This Lesson
• A 7-digit number has millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places.
• An 8-digit number has ten-millions, millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places.
• Example: 45,678,901 has 4 ten-millions, 5 millions, 6 hundred-thousands, 7 ten-thousands, 8 thousands, 9 hundreds, 0 tens, and 1 one.
• Expanded form: 45,678,901 = 40,000,000 + 5,000,000 + 600,000 + 70,000 + 8,000 + 900 + 0 + 1.
• Word form: 45,678,901 = "forty-five million six hundred seventy-eight thousand nine hundred one".
• The number 100,000,000 is the smallest 9-digit number (100 million).
Key Definitions:
• Digit: A single number symbol (0–9).
• Place Value: The value of a digit based on its position in the number.
• Ten-Millions: The eighth digit from the right (e.g., in 45,678,901, the 4 is in the ten-millions place).
• Millions: The seventh digit from the right (e.g., in 45,678,901, the 5 is in the millions place).
• Hundred-Thousands: The sixth digit from the right (e.g., in 45,678,901, the 6 is in the hundred-thousands place).
• Commas: Used in numbers to separate millions and thousands (e.g., 45,678,901).

Quick Reference: Place Value Chart

NumberTen-MillionsMillionsHundred-ThousandsTen-ThousandsThousandsHundredsTensOnesExpanded Form (abbreviated)
34,567,8903456789030,000,000 + 4,000,000 + 500,000 + 60,000 + 7,000 + 800 + 90 + 0
9,045,678090456780 + 9,000,000 + 0 + 40,000 + 5,000 + 600 + 70 + 8
70,203,4567020345670,000,000 + 0 + 200,000 + 0 + 3,000 + 400 + 50 + 6
99,999,9999999999990,000,000 + 9,000,000 + 900,000 + 90,000 + 9,000 + 900 + 90 + 9

Scroll sideways on smaller screens to view the full table.

Place Value (Ten-Millions, Millions, Hundred-Thousands, Ten-Thousands, Thousands, Hundreds, Tens, Ones)

Every 7-8 digit number has places for ten-millions, millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones. The ten-millions place tells how many groups of 10,000,000, the millions place tells how many groups of 1,000,000, the hundred-thousands place tells how many groups of 100,000, the ten-thousands place tells how many groups of 10,000, the thousands place tells how many groups of 1,000, the hundreds place tells how many groups of 100, the tens place tells how many groups of 10, and the ones place tells how many individual units.

Step-by-Step: Finding Place Value
1. Write the number and identify each digit from right to left.
2. The first digit (rightmost) is the ones place.
3. The second digit is the tens place.
4. The third digit is the hundreds place.
5. The fourth digit is the thousands place.
6. The fifth digit is the ten-thousands place.
7. The sixth digit is the hundred-thousands place.
8. The seventh digit is the millions place.
9. The eighth digit is the ten-millions place.
10. Multiply each digit by its place value and add them to get the number.
Place Value of 8-Digit Numbers 3 Ten-
Millions 4 Millions 5 Hundred-
Thousands 6 Ten-
Thousands 7 Thousands 8 Hundreds 9 Tens 0 Ones , , 34,567,890 = 30,000,000 + 4,000,000 + 500,000 + 60,000 + 7,000 + 800 + 90 + 0 3 ten-millions + 4 millions + 5 hundred-thousands + 6 ten-thousands + 7 thousands + 8 hundreds + 9 tens + 0 ones

The number 34,567,890 has 3 ten-millions, 4 millions, 5 hundred-thousands, 6 ten-thousands, 7 thousands, 8 hundreds, 9 tens, and 0 ones. It is the sum of 30,000,000, 4,000,000, 500,000, 60,000, 7,000, 800, 90, and 0.

Example 1: Identifying Place Value
Problem: What is the value of the digit 7 in the number 47,892,345?

Solution:
Step 1: Write the number: 47,892,345.

Step 2: The digits are 4, 7, 8, 9, 2, 3, 4, and 5. The 7 is in the millions place (seventh from the right).

Step 3: The value of 7 in the millions place is 7 × 1,000,000 = 7,000,000.

Answer: The value of 7 is 7,000,000.
Example 2: Building a Number
Problem: What number has 5 ten-millions, 2 millions, 8 hundred-thousands, 3 ten-thousands, 6 thousands, 9 hundreds, 4 tens, and 7 ones?

Solution:
Step 1: Write the ten-millions digit: 5.

Step 2: Write the millions digit: 2.

Step 3: Write the hundred-thousands digit: 8.

Step 4: Write the ten-thousands digit: 3.

Step 5: Write the thousands digit: 6.

Step 6: Write the hundreds digit: 9.

Step 7: Write the tens digit: 4.

Step 8: Write the ones digit: 7.

Step 9: Combine: 52,836,947.

Answer: The number is 52,836,947.
Watch Out!
Remember that the value of a digit depends on its position. The digit 3 in 34,567,890 has a value of 30,000,000, while in 54,367,890 it has a value of 3,000,000.

Practice for Place Value

  1. What is the value of the digit 6 in 61,392,478?
  2. What number has 8 ten-millions, 0 millions, 4 hundred-thousands, 2 ten-thousands, 5 thousands, 7 hundreds, 3 tens, and 1 one?
  3. In the number 90,415,678, what digit is in the hundred-thousands place?
  4. What is the value of the digit 9 in 29,870,456?
  5. Write the number with 7 ten-millions, 3 millions, 0 hundred-thousands, 8 ten-thousands, 7 thousands, 6 hundreds, 5 tens, and 4 ones.

Reading Numbers in Words

To read a 7-8 digit number in words, read the part before the first comma as one number and say "million", then read the part before the second comma and say "thousand", then read the remaining three digits. For 7-digit numbers, the first part is in millions.

Step-by-Step: Reading a 7-8 Digit Number
1. Read the digits before the first comma (the millions part) as one number and say "million".
2. Read the digits before the second comma (the thousands part) as one number and say "thousand".
3. Read the remaining three digits as a 3-digit number.
4. For numbers like 345,000,000, say "three hundred forty-five million".
5. Use hyphens between tens and ones (e.g., "sixty-seven").
Example 3: Reading Numbers in Words
Problem: Write the following numbers in words: 482,736,901; 605,000,000; 99,004,567.

Solution:
Step 1: 482,736,901 = four hundred eighty-two million seven hundred thirty-six thousand nine hundred one.

Step 2: 605,000,000 = six hundred five million.

Step 3: 99,004,567 = ninety-nine million four thousand five hundred sixty-seven.

Answer: 482,736,901 = four hundred eighty-two million seven hundred thirty-six thousand nine hundred one; 605,000,000 = six hundred five million; 99,004,567 = ninety-nine million four thousand five hundred sixty-seven.
Example 4: Writing Numbers from Words
Problem: Write the following as numbers: seven hundred twenty-three million four hundred fifty-six thousand seven hundred eighty-nine, eight hundred million two, five hundred sixty-seven million eight hundred thousand.

Solution:
Step 1: seven hundred twenty-three million four hundred fifty-six thousand seven hundred eighty-nine = 723,456,789.

Step 2: eight hundred million two = 800,000,002.

Step 3: five hundred sixty-seven million eight hundred thousand = 567,800,000.

Answer: 723,456,789; 800,000,002; 567,800,000.
Watch Out!
When reading numbers with zeros, be careful not to say "and" (e.g., 800,000,002 is "eight hundred million two", not "eight hundred million and two").

Practice for Reading Numbers in Words

  1. Write 621,895,347 in words.
  2. Write 900,040,000 in words.
  3. Write 710,000,005 in words.
  4. Write "three hundred fifty-five million eight hundred twenty-one thousand four hundred fifty-six" as a number.
  5. Write "four hundred thirty-three million five thousand" as a number.

Writing Numbers in Expanded Form

Expanded form shows the value of each digit in a number. For a 7-8 digit number, it is the sum of the ten-millions, millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones values.

Step-by-Step: Writing in Expanded Form
1. Identify the ten-millions digit and multiply it by 10,000,000.
2. Identify the millions digit and multiply it by 1,000,000.
3. Identify the hundred-thousands digit and multiply it by 100,000.
4. Identify the ten-thousands digit and multiply it by 10,000.
5. Identify the thousands digit and multiply it by 1,000.
6. Identify the hundreds digit and multiply it by 100.
7. Identify the tens digit and multiply it by 10.
8. Identify the ones digit.
9. Write the sum of these eight values.
Example 5: Expanded Form (8-Digit)
Problem: Write 83,672,541 in expanded form.

Solution:
Step 1: Ten-millions digit is 8 → 8 × 10,000,000 = 80,000,000.

Step 2: Millions digit is 3 → 3 × 1,000,000 = 3,000,000.

Step 3: Hundred-thousands digit is 6 → 6 × 100,000 = 600,000.

Step 4: Ten-thousands digit is 7 → 7 × 10,000 = 70,000.

Step 5: Thousands digit is 2 → 2 × 1,000 = 2,000.

Step 6: Hundreds digit is 5 → 5 × 100 = 500.

Step 7: Tens digit is 4 → 4 × 10 = 40.

Step 8: Ones digit is 1 → 1.

Step 9: Sum: 80,000,000 + 3,000,000 + 600,000 + 70,000 + 2,000 + 500 + 40 + 1.

Answer: 83,672,541 = 80,000,000 + 3,000,000 + 600,000 + 70,000 + 2,000 + 500 + 40 + 1.
Example 6: Expanded Form (7-Digit)
Problem: Write 9,045,678 in expanded form.

Solution:
Step 1: Millions digit is 9 → 9 × 1,000,000 = 9,000,000.

Step 2: Hundred-thousands digit is 0 → 0 × 100,000 = 0.

Step 3: Ten-thousands digit is 4 → 4 × 10,000 = 40,000.

Step 4: Thousands digit is 5 → 5 × 1,000 = 5,000.

Step 5: Hundreds digit is 6 → 6 × 100 = 600.

Step 6: Tens digit is 7 → 7 × 10 = 70.

Step 7: Ones digit is 8 → 8.

Step 8: Sum: 9,000,000 + 0 + 40,000 + 5,000 + 600 + 70 + 8.

Answer: 9,045,678 = 9,000,000 + 0 + 40,000 + 5,000 + 600 + 70 + 8.
Watch Out!
Make sure to include zeros in expanded form if a digit is zero. For example, 40,502,000 = 40,000,000 + 0 + 500,000 + 0 + 2,000 + 0 + 0 + 0.

Practice for Expanded Form

  1. Write 562,438,791 in expanded form.
  2. Write 700,406,000 in expanded form.
  3. Write 91,100,045 in expanded form.
  4. What number is 400,000,000 + 30,000,000 + 2,000,000 + 500,000 + 60,000 + 7,000 + 800 + 90?
  5. What number is 800,000,000 + 0 + 0 + 700,000 + 0 + 3,000 + 0 + 5?

Comparing & Ordering Numbers

To compare 7-8 digit numbers, compare the ten-millions digits first. If they are equal, compare the millions digits, then hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones. Use symbols: > (greater than), < (less than), = (equal to).

Step-by-Step: Comparing Numbers
1. Compare the ten-millions digits. The larger digit means the number is larger.
2. If the ten-millions digits are equal, compare the millions digits.
3. If the millions digits are also equal, compare the hundred-thousands digits.
4. Continue with ten-thousands, thousands, hundreds, tens, and ones.
5. Use <, >, or = to show the relationship.
Example 7: Comparing Numbers
Problem: Compare 45,678,901 and 45,678,912.

Solution:
Step 1: Both have 4 in the ten-millions place.

Step 2: Both have 5 in the millions place.

Step 3: Both have 6 in the hundred-thousands place.

Step 4: Both have 7 in the ten-thousands place.

Step 5: Both have 8 in the thousands place.

Step 6: Both have 9 in the hundreds place.

Step 7: Compare tens: 0 vs 1. 0 is less than 1, so 45,678,901 < 45,678,912.

Answer: 45,678,901 < 45,678,912.
Example 8: Ordering Numbers
Problem: Order these numbers from least to greatest: 389,756,124; 390,012,345; 389,750,999; 391,100,000.

Solution:
Step 1: Compare ten-millions: all have 3.

Step 2: Compare millions: 389,xxx,xxx and 390,xxx,xxx. So 389,xxx,xxx < 390,xxx,xxx < 391,100,000.

Step 3: For 389,xxx,xxx: compare hundred-thousands: 7 vs 7 (equal). Compare ten-thousands: 5 vs 5 (equal). Compare thousands: 6 vs 0. 389,750,999 < 389,756,124.

Step 4: Order: 389,750,999; 389,756,124; 390,012,345; 391,100,000.

Answer: 389,750,999; 389,756,124; 390,012,345; 391,100,000.
Watch Out!
When comparing numbers, always start with the highest place value (ten-millions). Do not compare ones digits first!

Practice for Comparing & Ordering

  1. Compare: 612,345,678 ☐ 612,345,687 (use >, <, or =)
  2. Compare: 800,070,000 ☐ 800,700,000
  3. Compare: 999,999,999 ☐ 999,999,998
  4. Order these from greatest to least: 456,000,000; 456,500,000; 455,999,999; 456,001,000.
  5. Order these from least to greatest: 123,456,789; 123,654,789; 123,546,789; 123,465,789.

Rounding Large Numbers

Rounding helps us estimate very large numbers quickly. To round a number, look at the digit to the right of the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down.

Step-by-Step: Rounding Numbers
1. Identify the place value you are rounding to (e.g., nearest million).
2. Look at the digit to the right of that place.
3. If that digit is 5 or more, add 1 to the rounding digit and change all digits to the right to zero.
4. If that digit is 4 or less, keep the rounding digit the same and change all digits to the right to zero.
Example 9: Rounding to the Nearest Million
Problem: Round 345,678,901 to the nearest million.

Solution:
Step 1: Identify the millions place: 5 (in 345,678,901).

Step 2: Look at the digit to the right (hundred-thousands place): 6.

Step 3: 6 is 5 or more, so round up: 5 becomes 6.

Step 4: Change all digits to the right to zero: 346,000,000.

Answer: 345,678,901 rounded to the nearest million is 346,000,000.
Example 10: Rounding to the Nearest Ten-Million
Problem: Round 782,345,678 to the nearest ten-million.

Solution:
Step 1: Identify the ten-millions place: 8 (in 782,345,678).

Step 2: Look at the digit to the right (millions place): 2.

Step 3: 2 is 4 or less, so round down: 8 stays 8.

Step 4: Change all digits to the right to zero: 780,000,000.

Answer: 782,345,678 rounded to the nearest ten-million is 780,000,000.
Example 11: Rounding to the Nearest Hundred-Million
Problem: Round 456,789,123 to the nearest hundred-million.

Solution:
Step 1: Identify the hundred-millions place: 4 (in 456,789,123).

Step 2: Look at the digit to the right (ten-millions place): 5.

Step 3: 5 is 5 or more, so round up: 4 becomes 5.

Step 4: Change all digits to the right to zero: 500,000,000.

Answer: 456,789,123 rounded to the nearest hundred-million is 500,000,000.
Watch Out!
When rounding, remember to change all digits to the right of the rounding place to zero. Do not forget the zeros!

Practice for Rounding

  1. Round 456,789,123 to the nearest million.
  2. Round 234,567,890 to the nearest ten-million.
  3. Round 899,999,999 to the nearest hundred-million.
  4. Round 999,999,999 to the nearest ten-million.
  5. Round 345,678,901 to the nearest hundred-thousand.

Cumulative Practice Exercises

  1. What is the value of the digit 9 in 934,278,561?
  2. Write 745,206,893 in words.
  3. Write 800,000,030 in expanded form.
  4. Compare: 654,321,789 ☐ 654,321,798 (use >, <, or =)
  5. Order these numbers from least to greatest: 234,567,890; 234,657,890; 234,576,890; 234,765,890.
  6. What number is 600,000,000 + 40,000,000 + 3,000,000 + 200,000 + 70,000 + 8,000 + 900 + 50?
  7. Write "eight hundred ninety-nine million five hundred seventy-one thousand three hundred forty-two" as a number.
  8. What is the value of the digit 4 in 746,823,915?
  9. Write 900,000,017 in expanded form.
  10. Compare: 830,000,001 ☐ 830,000,010 (use >, <, or =)
  11. Order these from greatest to least: 555,555,555; 555,555,505; 555,555,550; 555,555,500.
  12. What number has 7 ten-millions, 2 millions, 8 hundred-thousands, 0 ten-thousands, 7 thousands, 0 hundreds, 4 tens, and 5 ones?
  13. Write 123,045,678 in words.
  14. What is the value of the digit 6 in 167,895,432?
  15. Compare: 999,999,999 ☐ 1,000,000,000 (use >, <, or =)
  16. Round 234,567,890 to the nearest million.
  17. Round 789,123,456 to the nearest ten-million.
  18. Round 456,789,123 to the nearest hundred-million.
  19. Round 123,456,789 to the nearest hundred-thousand.
  20. Round 999,999,999 to the nearest hundred-million.
Show/Hide Answers

Solutions to Cumulative Exercises

  1. Step 1: In 934,278,561, the 9 is in the hundred-millions place.
    Answer: 900,000,000.
  2. Step 1: 745,206,893 = seven hundred forty-five million two hundred six thousand eight hundred ninety-three.
    Answer: seven hundred forty-five million two hundred six thousand eight hundred ninety-three.
  3. Step 1: 800,000,030 = 800,000,000 + 0 + 0 + 0 + 0 + 0 + 30 + 0.
    Answer: 800,000,000 + 0 + 0 + 0 + 0 + 0 + 30 + 0.
  4. Step 1: 654,321,789 vs 654,321,798: ten-millions same (6), millions same (5), hundred-thousands same (4), ten-thousands same (3), thousands same (2), hundreds same (1), tens: 8 vs 9. 654,321,789 < 654,321,798.
    Answer: 654,321,789 < 654,321,798.
  5. Step 1: All in the 234,000,000s. Order: 234,567,890; 234,576,890; 234,657,890; 234,765,890.
    Answer: 234,567,890; 234,576,890; 234,657,890; 234,765,890.
  6. Step 1: 600,000,000 + 40,000,000 + 3,000,000 + 200,000 + 70,000 + 8,000 + 900 + 50 = 643,278,950.
    Answer: 643,278,950.
  7. Step 1: eight hundred ninety-nine million = 899,000,000; five hundred seventy-one thousand = 571,000; three hundred forty-two = 342.
    Answer: 899,571,342.
  8. Step 1: In 746,823,915, the 4 is in the ten-millions place.
    Answer: 40,000,000.
  9. Step 1: 900,000,017 = 900,000,000 + 0 + 0 + 0 + 0 + 0 + 10 + 7.
    Answer: 900,000,000 + 0 + 0 + 0 + 0 + 0 + 10 + 7.
  10. Step 1: 830,000,001 vs 830,000,010: ten-millions same (8), millions same (3), hundred-thousands same (0), ten-thousands same (0), thousands same (0), hundreds same (0), tens: 0 vs 1. 830,000,001 < 830,000,010.
    Answer: 830,000,001 < 830,000,010.
  11. Step 1: All in the 555,555,000s. Order: 555,555,555; 555,555,550; 555,555,505; 555,555,500.
    Answer: 555,555,555; 555,555,550; 555,555,505; 555,555,500.
  12. Step 1: 7 ten-millions = 70,000,000; 2 millions = 2,000,000; 8 hundred-thousands = 800,000; 0 ten-thousands = 0; 7 thousands = 7,000; 0 hundreds = 0; 4 tens = 40; 5 ones = 5.
    Answer: 72,807,045.
  13. Step 1: 123,045,678 = one hundred twenty-three million forty-five thousand six hundred seventy-eight.
    Answer: one hundred twenty-three million forty-five thousand six hundred seventy-eight.
  14. Step 1: In 167,895,432, the 6 is in the ten-millions place.
    Answer: 60,000,000.
  15. Step 1: 999,999,999 vs 1,000,000,000: compare ten-millions: 9 vs 1 (with carry). 999,999,999 < 1,000,000,000.
    Answer: 999,999,999 < 1,000,000,000.
  16. Step 1: 234,567,890 rounded to nearest million: millions digit is 4, look at hundred-thousands: 5 (round up). 234,000,000 + 1,000,000 = 235,000,000.
    Answer: 235,000,000.
  17. Step 1: 789,123,456 rounded to nearest ten-million: ten-millions digit is 8, look at millions: 9 (round up). 789,000,000 + 10,000,000 = 790,000,000.
    Answer: 790,000,000.
  18. Step 1: 456,789,123 rounded to nearest hundred-million: hundred-millions digit is 4, look at ten-millions: 5 (round up). 456,000,000 + 100,000,000 = 500,000,000.
    Answer: 500,000,000.
  19. Step 1: 123,456,789 rounded to nearest hundred-thousand: hundred-thousands digit is 4, look at ten-thousands: 5 (round up). 123,400,000 + 100,000 = 123,500,000.
    Answer: 123,500,000.
  20. Step 1: 999,999,999 rounded to nearest hundred-million: hundred-millions digit is 9, look at ten-millions: 9 (round up). 999,000,000 + 100,000,000 = 1,000,000,000.
    Answer: 1,000,000,000.

Conclusion & Summary

Reading and writing 7-8 digit numbers is an essential skill for working with very large quantities. By understanding place value up to the ten-millions, you can read any number up to 99,999,999, write it in expanded form, compare numbers, and round them. These skills are crucial for understanding national budgets, population statistics, and scientific measurements.

Key Takeaways:
1. Place Value: 7-8 digit numbers have ten-millions, millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places.
2. Reading: Say the ten-millions, millions, hundred-thousands, and thousands, then "million" and "thousand", then the remaining three digits.
3. Expanded Form: 45,678,901 = 40,000,000 + 5,000,000 + 600,000 + 70,000 + 8,000 + 900 + 0 + 1.
4. Comparing: Compare ten-millions first, then millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones.
5. Rounding: Look at the digit to the right of the rounding place; 5 or more rounds up.

Keep practicing with large numbers—you'll see them in population counts, national budgets, and scientific measurements!

Video Resource

Watch this video for more examples of reading and writing large numbers.

Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c